The propagation of electron fluxes in the solar corona

The problem of energetic electron flux propagation in the solar coronal plasma is solved with due regard for the influence of the oppositely directed neutralizing cold electron flux and the kinematic escape effect of the electrons with different velocities. It is shown that the flux electrons are accelerated in the process of propagation, thus forming a beam, whose velocity is constant on rather long time scales. Three regimes can be realized in this case. In the first regime, plasma waves do not have time to be excited because they escape rapidly from resonance with the beam. In the second regime, waves are excited, but the beam does not have time to relax. The third regime is quasi-linear relaxation.The generation of solar type III radio bursts in the second regime of electron flux propagation is considered.     

Improved three-dimensional mapping of the electron density distribution of the solar corona

Three-dimensional maps of the distribution of coronal electron density can now be computed with two radial functions in the series expansion for the density (rather than with only one radial function as shown in our previous paper). With the improved maps we can determine the topological variation of the electron density with radial distance, and thus can (1) distinguish coronal condensations from coronal streamers, (2) trace the structure of a streamer as a function of height, and (3) determine the non-radial orientation of a streamer. We summarize the previous work in concise mathematical notation, show examples of the improved maps derived from two radial functions, and discuss in detail the expectations and limitations of the method. Of great utility are computer-simulated pictures showing the solar corona as it would appear if veiwed from above the north (or south) pole.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The stability of electron beams in the flaring solar corona

The conditions required for the stability of a steady-state electron beam propagating in the solar corona are determined using the quasi-linear theory. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution function being given by an analytic solution of the linearized Fokker-Planck equation. It is shown that, when the gyrofrequency is less than the plasma frequency, the instability has a narrow angular range, with the maximum growth rate occuring along the magnetic field. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of the results for alternative models of hard X-ray bursts are discussed and it is argued that Langmuir instability will not occur on either the trap model or the thermal model. Such models would, therefore, be refuted by the detection of a large flux of plasma microwave radiation associated with hard X-ray emission.     

On determining the electron density distribution of the solar corona from K-coronameter data

The electron density distribution of the inner solar corona (r 2 R ) as a function of latitude, longitude, and radial distance is determined from K-coronameter polarization-brightness (pB) data. A Legendre polynomial is assumed for the electron density distribution, and the coefficients of the polynomial are determined by a least-mean-square regression analysis of several days of pB-data. The calculated electron density distribution is then mapped as a function of latitude and longitude. The method is particularly useful in determining the longitudinal extent of coronal streamers and enhancements and in resolving coronal features whose projections on the plane of the sky overlap.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Differential rotation of the solar electron corona

Autocorrelation analyses of K-coronameter observations made at Haleakala and Mauna Loa, Hawaii, during 1964–1967 have established average yearly rotation rates of coronal features as a function of latitude and height above the limb. At low latitudes the corona was found to rotate at the same rate as sunspots but at higher latitudes was consistently faster than the underlying photosphere. There were differences as large as 3–4% in the rate at specific latitudes from year to year and between the two hemispheres. In 1967 a nearly constant rotation was found for heights ranging from 1.125 to 2.0 R ₀. For 1966 there was a more complicated pattern of height dependence, with the rate generally decreasing with height at low latitudes and increasing at high latitudes.At Hawaii Institute of Geophysics.     

The influence of doubly excited levels on the ionization formula for the solar corona

The existence of doubly excited levels causes dielectronic recombination and autoionization. These effects influence respectively the total recombination rate and the total ionization rate of different ions. The ratios of dielectronic recombination to radiative recombination and of autoionization to collisional ionization are given as a function of the electron temperature for the term systems of Oiv, Ov, Ovi, Siix and Fexv. While autoionization can contribute appreciably to the total ionization rate, dielectronic recombination is always the most effective recombination mechanism.     

On the temperature distribution in the solar corona

An improved value of coronal temperature is obtained by the degree of ionization method taking various processes into consideration. Comparison with some of the existing results has also been made.     

Radial variation of differential rotation in the solar electron corona

Long-lived brightness structures in the solar electron corona persist over many solar rotation periods and permit an observational determination of coronal magnetic tracer rotation as a function of latitude and height in the solar atmosphere. For observations over 1964–1976 spanning solar cycle 20, we compare the latitude dependence of rotation at two heights in the corona. Comparison of rotation rates from East and West limbs and from independent computational procedures is used to estimate uncertainty. Time-averaged rotation rates based on three methods of analysis demonstrate that, on average, coronal differential rotation decreases with height from 1.125 to 1.5 R _S. The observed radial variation of differential rotation implies a scale height of approximately 0.7 R _S for coronal differential rotation.Model calculations for a simple MHD loop show that magnetic connections between high and low latitudes may produce the observed radial variations of magnetic tracer rotation. If the observed tracer rotation represents the rotation of open magnetic field lines as well as that of closed loops, the small scale height for differential rotation suggests that the rotation of solar magnetic fields at the base of the solar wind may be only weakly latitude dependent. If, instead, closed loops account completely for the radial gradients of rotation, outward extrapolation of electron coronal rotation may not describe magnetic field rotation at the solar wind source. Inward extrapolations of observed rotation rates suggest that magnetic field and plasma are coupled a few hundredths of a solar radius beneath the photosphere.     

Dynamics of electron beams in the inhomogeneous solar corona plasma

Dynamics of a spatially-limited electron beam in the inhomogeneous solar corona plasma is considered in the framework of weak turbulence theory when the temperature of the beam significantly exceeds that of surrounding plasma. The numerical solution of kinetic equations manifests that generally the beam accompanied by Langmuir waves propagates as a beam-plasma structure with a decreasing velocity. Unlike the uniform plasma case the structure propagates with the energy losses in the form of Langmuir waves. The results obtained are compared with the results of observations of type III bursts. It is shown that the deceleration of type III sources can be explained by corona inhomogeneity. The frequency drift rates of the type III sources are found to be in good agreement with the numerical results of beam dynamics.     

A method for the evaluation of the brightness distribution in the solar corona

With photography of the solar corona at eclipses as an example, a method is given to calculate the relative brightnesses along a solar radius from a set of photographs. This set must be taken with different exposures, the ratio of two successive exposures, however, being constant. From the photometry of the density the relative brightnesses can be derived by a procedure consisting of three steps:

1. Reconstruction of a differential characteristic curve,
2. Compensation of the whole set of photographs. This leads to a discrete number of density-values to be associated with the relative brightnesses of the corona. For an arbitrary density-value
3. an improved method of interpolation based on the least square method is required. The procedure can more easily be carried out by computer-analysis.

     

The heating of the solar corona

The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona. Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed.Received: 6 February 2003, Published online: 14 November 2003 Correspondence to: R. W. Walsh     

The spectrum of Nixix in the solar corona

The wavelengths and intensities of the stronger transitions in the spectrum of Ni xix are reduced from measurements of the X-ray spectra of three coronal active regions. The new measured wavelengths are consistent with prediction by isoelectronic extrapolation from the wavelengths of well established transitions but are about 0.01 Å longer than previously accepted laboratory measurements. This difference appears to be crucial to the correct assignment of features in the coronal spectrum to Ni xix. The relative intensities of our new assignments to Ni xix are in broad agreement with the Loulergue-Nussbaumer calculations.     

The nonlinear acceleration of a magnetic disturbance in the solar corona

The simple form of Ohm's law (SI units)J = (E+ v × B)is valid for high density magnetofluids (where the mean free path for collisions is less than the Larmor radius) but is not strictly valid for the tenuous solar corona. We examine the nonlinear evolution of a magnetic disturbance using a more general form of Ohm's law which includes the Hall term. The Hall term dominates MHD development in the corona when the product of the magnetic scale length and the square root of the density is small enough; in particular when (1) the electron density is less than about 10¹³ m^-3 and (2) the scale length is less than a few hundred meters. For these parameters, a magnetic disturbance may carry electrons at a drift speed in excess of the Alfvén speed. We believe this nonlinear phenomenon may be important for the impulsive acceleration of charged particles in the solar corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Structures in a non-magnetic solar corona

A fluid mechanical convective instability is examined under the conditions found in the solar corona. Linearized density perturbations are shown to grow as they are carried outward by the solar wind. The non-linear instability may be proposed as a cause of coronal structures in non-magnetic stars, or in regions of the solar corona with weak magnetic fields.     

On a cold emission in the solar corona

The faint emission of hydrogen, helium and metals in the corona which appeared near an active prominence is studied. The calculations showed that the temperature of the emission region is in the limits from 10 000 K to 30 000 K and the electron density is between 10⁹-10¹⁰ cm^-3, respectively.     

Electrons in the solar corona

During a balloon flight in France on September 13, 1971, at altitude 32 000 m, the solar corona was cinematographed from 2 to 5R during 5 hr, with an externally occulted coronagraph.Motions in coronal features, when they occur, exhibit deformations of structures with velocities not exceeding a few 10 km s^–1; several streamers were often involved simultaneously; these variations are compatible with magnetic changes or sudden reorganizations of lines of forces.Intensity and polarization measurements give the electron density with height in the quiet corona above the equator. Electron density gradient for one of the streamers gives a temperature of 1.6 × 10⁶ K and comparisons with the on-board Apollo 16 coronal observation of 31 July, 1971 are compatible with the extension of this temperature up to 25 R _bd.Three-dimensional structures and localizations of the streamers are deduced from combined photometry, polarimetry and ground-based K coronametry. Three of the four coronal streamers analysed have their axis bent with height towards the direction of the solar rotation, as if the upper corona has a rotation slightly faster than the chromosphere.     

Electrons in the solar corona

We discuss a model for the formation of the chromospheric Ca ii K line which does not make the usual assumption of complete redistribution. Using a physically reasonable scattering model, we find significant departures due to the frequency dependence of the line source function, particularly in the relative intensity and centre-to-limb behaviour of the K₁ parts of the line and in the asymmetry produced by differential velocity fields. We conclude that the frequency dependence of the K line source function must be considered in quantitative models for the formation of the K line.     

Electrons in the solar corona

The polarimetric survey of electrons in the K-corona initiated at Pic-du-Midi and Meudon Observatories in 1964 now covers a full solar cycle of activity. The measurements are photometrically calibrated in an absolute scale.In June 1967 a persistent coronal feature was fan-shaped as a lame coronale above quiescent prominences. We deduce an electron density of N ₀ = 1.5 × 10⁸ at 60 000 km above the photosphere, a total number of 14 × 10³⁹ electrons, a hydrostatic temperature of 1.7 × 10⁶ K, and a total thermal energy 3N _eKT = 1.0 × 10³¹ ergs. When a center of activity appeared, a major localized condensation developed to replace the old elongated feature, with N ₀ = 4.5 × 10⁸, a total of 4.5 × 10³⁹ electrons and the same temperature of 1.7 × 10⁶ K.Also, a fan-shaped feature of exceptional intensity was analysed on 8 September 1966, with N ₀ = 6 × 10⁸ and a total of 24 × 10³⁹ electrons.Fan-shaped features are frequent above quiescent prominences. They degenerate above a height of 2R into thinner isolated columns or blades with temperatures also around 1.7 × 10⁶ K.     

Energy balance of the corona and the origin of quasi-stationary high-speed solar wind streams

The energy balance of open-field regions of the corona and solar wind and the influence of the flow geometry in the corona upon the density and temperature, are analyzed. It is found that the energy flux arriving at the corona is constant for the corona's open regions with different flow geometries. For the waves heating the corona and solar wind, the dependence of the absorption coefficient on the corona's plasma density is found to be within the range of distances r=1.05–1.5R . It is shown that the wave absorption is more dependent on electron density than the coronal emission. It is this difference that causes lower-density coronal holes to be colder than quiet regions. It is found that the additional energy flux necessary for providing energy balance of the corona and for producing solar wind is a flux of Alfvén waves, which can provide the energy needed for producing quasi-stationary high-speed solar wind streams. Theoretical models of coronal holes and the question of why the high-speed solar wind streams are precisely flowing out of coronal holes, are discussed.     

The solar wind and the temperature-density structure of the solar corona

The influence of the solar wind on large-scale temperature and density distributions in the lower corona is studied. This influence is most profoundly felt through its effect upon the geometry of coronal magnetic fields since the presence of expansion divides the corona into magnetically open and closed regions. Each of these regions is governed by entirely different energy transport processes. This results in significant temperature differences since only the open field regions suffer outward conductive heat losses. Because the temperature influences the density in an exponential manner, large density inhomogeneities are to be expected.An approximate method for calculating the temperature and density distribution in a known magnetic field geometry is outlined and numerical estimates are carried out for representative coronal conditions. These estimates show that temperature differences of a factor of about two and density differences of ten can be expected in the lower corona even for uniform base conditions. As a result, we do not regard the so-called coronal holes necessairly as locations of reduced mechanical heating. Alternatively, we suggest that they are regions of open magnetic field lines being continuously drained of energy contert by the solar wind expansion and outward thermal conduction.The National Center for Atmospheric Research is sponsored by the National Science Foundation.